There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ 25(1 - sqrt(1 + (\frac{1}{(tan(x))})))(1 - {(tan(x))}^{2})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 25tan^{2}(x)sqrt(\frac{1}{tan(x)} + 1) - 25sqrt(\frac{1}{tan(x)} + 1) - 25tan^{2}(x) + 25\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 25tan^{2}(x)sqrt(\frac{1}{tan(x)} + 1) - 25sqrt(\frac{1}{tan(x)} + 1) - 25tan^{2}(x) + 25\right)}{dx}\\=&25*2tan(x)sec^{2}(x)(1)sqrt(\frac{1}{tan(x)} + 1) + \frac{25tan^{2}(x)(\frac{-sec^{2}(x)(1)}{tan^{2}(x)} + 0)*\frac{1}{2}}{(\frac{1}{tan(x)} + 1)^{\frac{1}{2}}} - \frac{25(\frac{-sec^{2}(x)(1)}{tan^{2}(x)} + 0)*\frac{1}{2}}{(\frac{1}{tan(x)} + 1)^{\frac{1}{2}}} - 25*2tan(x)sec^{2}(x)(1) + 0\\=&50tan(x)sqrt(\frac{1}{tan(x)} + 1)sec^{2}(x) - \frac{25sec^{2}(x)}{2(\frac{1}{tan(x)} + 1)^{\frac{1}{2}}} + \frac{25sec^{2}(x)}{2(\frac{1}{tan(x)} + 1)^{\frac{1}{2}}tan^{2}(x)} - 50tan(x)sec^{2}(x)\\ \end{split}\end{equation} \]

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